The Kerr/CFT Correspondence

TL;DR

This paper demonstrates that the near-horizon quantum states of an extreme Kerr black hole can be described by a two-dimensional conformal field theory, providing a microscopic explanation for black hole entropy through holographic duality.

Contribution

It establishes the existence of a Virasoro algebra with a specific central charge near the horizon of an extreme Kerr black hole, linking black hole entropy to a dual CFT description.

Findings

Virasoro algebra with central charge c_L=12J/ħ found near horizon

Microscopic entropy matches Bekenstein-Hawking entropy via Cardy formula

Extreme Kerr black holes are conjectured to be holographically dual to a chiral 2D CFT

Abstract

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / \hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}.